Electronics II. Midterm II


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1 The University of Toledo su7ms_elct7.fm  Electronics II Midterm II Problems Points Total 0 Was the exam fair? yes no
2 The University of Toledo su7ms_elct7.fm  Problem 7 points Equation () specifies the expression of the amplification transfer function of a given feedback amplifier. A F (s) K F (s + )(s + 0 ) K F [rad/s].4π 0 4 rad/s () Problem Statement For the given amplification transfer function of equation (), demonstrate an ability to:. determine the midband gain A FO in db,. determine the values of the lower and upper angular cutoff frequencies, L and H, of the magnitude A F () of A F (s), 3. determine the bandwidth of the amplifier whose amplification transfer function is given by (). 4. Prepare an asymptotic Bode plot of the amplification s magnitude A F (). Hint # For full credit: all equations, all answers to questions, all circuit models and other graphical representations are expected to be entered into the space designated for them; all shown numerical results must be preceded by the symbolic and numeric expressions whose evaluation produces the shown results. Problem Solution An explicit demonstration of understanding the following solution steps is expected.. Determine the numerical values of zeros and poles of the amplification transfer function given as equation (). Show your work and the results in the space reserved for equation (). By inspection of the function (), one concludes that it does not include any zeros. () p  .4π 0 4 rad/s p π π 0 6 rad/s /5/7
3 The University of Toledo su7ms_elct7.fm  3. Determine the value of the midband gain, A FO, in db. Show the necessary calculations in the space reserved for equation (3). K F K A F (s) F A FO (s + )(s + ) s s (+ )(+ ) (+ s s )(+ ) K F A FO.4π 0 4.4π (3) A FO A FO A FO [db] 0lg A FO 0 lg db.3 Prepare the expression of the amplification/gain A F (s) when sj, and following this, prepare the expression for the magnitudes A F (j) and A F () A F (j). Show the necessary calculations in the space reserved for equation (4). A F (s) A sj F (j) (+ j ) A FO (+ j ) (4) A F () A F (j) + ( ) A FO + ( ).4 Prepare the expression for calculating the db value of the magnitude A F () of the given transfer function (). Show the necessary calculations in the space reserved for equation (5). A F () [db] 0lgA F () 0lgA FO 0lg + ( ) 0lg + ( ) (5) /5/7
4 0.5 The University of Toledo su7ms_elct7.fm Based on the determined values of poles of A F (s), and the expressions (4) and/or (5), determine lower and upper cutoff angular frequencies, L and H, of the magnitude, A F (), of the given transfer function (). Show the necessary calculations in the space reserved for equation (6). L 0 rad/s H.4π 0 4 rad/s (6).6 Prepare the expression and calculate the bandwidth of the feedback amplifier whose transfer function is given in (). Show in the space reserved for equation (7), the necessary calculations for expressing the bandwidth in the Hz frequency unit. 0.5 BW f H  L π.4π(0 40) π khz (7).7 Using the prepared expression (5), prepare the asymptotic Bode Plot of the amplitude characteristic A f () of the given transfer function (). Show the prepared Bode plot in the space reserved for Figure.. A F ()[db] H lg Figure. Asymptotic Bode Plot of the magnitude A f () of the given transfer function A f (s). /5/7
5 The University of Toledo su7ms_elct7.fm  5 Problem 7 points Given is the electric circuit model of a Reference Current Source cell shown in Figure.(a). 0.7V V CC 6V r o 30kΩ r π 5Ω β o V +  E +  V CC B +  V CC 0V R int R int C (a) (b) Figure. BJT Reference Current Source cell s elerctrical circuit model. (a) The complete circuit model. (b)nonlinear AC model for the model in Figure.(a). Problem Statement For the given electric circuit model of Figure.(a), demonstrate an ability to:. prepare and use in analysis the smallsignal linearized models of BJTs,. determine an expression for the internal AC resistance, R int, of the given reference current source and determine its value. Hint # For full credit: all equations, all answers to questions, all circuit models and other graphical representations are expected to be entered into the space designated for them; all shown numerical results must be preceded by the symbolic and numeric expressions whose evaluation produces the shown results. Problem Solution For full credit, explicit demonstration of understanding the following solution steps is expected Label on the circuit models in Figures.(a),.(b) and.(b) the locations of the three transistor terminals: B, C, and E... Prepare the nonlinear AC circuit model of the circuit model shown in Figure.(a). Show the prepared model in the space reserved for Figure.(b)..3 Prepare the smallsignal equivalent circuit model of the BJT transistor, and show the prepared model in the space reserved for Figure.(a). /5/7
6 The University of Toledo su7ms_elct7.fm Prepare the smallsignal, linearized AC circuit model for the circuit model shown in Figure.(a), and show the prepared model in the space reserved for Figure.(b). B i b i c C E r π i e i b B 0.5 v be r π (a) β o i b E r o v ce β o i b Figure. Reference Current Source circuit models. (a) Smallsignal model of the MOSFET transistor. (b)smallsignal linearized AC model of the BJT Reference Current Source shown in Figure.(a). Hint # Notice that in the equivalent circuits of Figures.(b) and.(b) the internal AC resistance, R int, of the analyzed Reference Current Source appears between nodes C and E. As a consequence, the remaining steps for determining R int are:.5 through.6..5 Modify the circuit model of Figure.(b) by addingto it a test current source, i t, connected between the nodes C and E, with its current flowing into node C. (b) r o i c C v t i t.6 Prepare the equation(s) that solve the modified circuit of Figure.(b) for the voltage v t that appears across the current source i t and has the active convention positive reference direction with respect to i t. Show the necessary symbolic and numerical calculations in the space reserved for equations (). Since in the final circuit model of Figure.(b) resistor r π is short circuited: (a) no current flows through the resistor r π which sets i b 0A, (b) the current of the current source β o i b is set to β o i b 0A, (c) since no current flows through the current source β o i b, its internal resistance cteates an open circuit, and the entire collector current flows through the resistance r o. Therefore, v t r o i t () R int v t i r o 30kΩ t /5/7
7 The University of Toledo su7ms_elct7.fm  7 Problem 3 6 points The electric circuit model of the basic current mirror is shown in Figure V CC Reminder I C I B Q I B I O I B e IC Q R O V CC 0V I S β F V T I C β F I B I C I S e V T (+ VCE ) β F I C I B β FO (+ V CE ) Figure 3. Electric circuit model of a Basic current mirror. 0.5 Problem Statement Based on the shown current mirror s electric circuit model of Figure 3., demonstrate an ability to prepare:. The defining symbolic expression of the Mirror Ratio (MR) of a current mirror circuit;. the symbolic expression of the Mirror Ratio in the circuit of the basic current mirror. Hint # For full credit, give answers to all questions, prepare all required circuit diagrams, write all equations for which the space has been reserved, and show all symbolic and numerical expressions whose evaluation produces shown numerical results. Problem Solution For full credit, explicit demonstration of understanding the following solution steps is expected. 3. Prepare the defining symbolic expression of the quality metric Mirror Ratio (MR) of current mirror circuits. Show the prepared expression in the space reserved for equation (3). MR I O (3) 3. Indicate in the basic current mirror s circuit model of Figure 3. the positive reference directions of the base and collector currents of transistors Q and Q. /5/7
8 0.5 The University of Toledo su7ms_elct7.fm Prepare the relation between the collectoremitter voltage V CE of the transistor Q.and the voltage indicated in the circuit model of Figure 3. Show the prepared expressions in the space reserved for equation (3) V CE (3) 3.4 Based on the relations shown in Reminder section of Figure 3., prepare the expressions of the base and collector currents of transistors Q and Q. Show the prepared expressions in the space reserved for equations (33). I C I S e V T (+ VCE ) I C I S e V T (+ VCE ) I B I C β F I S e V T (+ V CE ) β FO (+ V CE ) V I BE S β e V T FO (33) I B V I BE S β e V T FO 3.5 Prepare the KCL equation for the node of the collector terminal of transistor Q and solve it for the current ; then substitute into it the expressions for collector and base currents derived under (33), and simplify/rearrange the result. Show your work in the space reserved for equations (34) KCL: I C + I B + I B (34) I e V T (+ VCE S ) + I S β FO V T e I S e V T V CE (+ + ) β FO /5/7
9 The University of Toledo su7ms_elct7.fm Using the so far prepared relations and expressions, prepare the expression of the Mirror Ratio MR for the Basic current mirror circuit of Figure 3. MR. Show your calculation in the space reserved for equation (35). (35) MR I O I C I C I C + I B + I B I S I e V S T e V T (+ V CE ) V CE (+ + ) β FO V CE + VA + + β FO /5/7
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